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Journal of the Ramanujan Mathematical Society

Volume 36, Issue 3, September 2021  pp. 221–229.

Hodge locus and Brill-Noether type locus

Authors:  Indranil Biswas and Ananyo Dan
Author institution:School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India

Summary:  The aim in this article is to study effective Cartier divisors D in a smooth projective variety X that satisfy the property that for any infinitesimal deformation X{t} of X, the divisor D lifts to an effective Cartier divisor on X{t} if and only if the cohomology class of the divisor D lifts to a Hodge class. This question is related to a classical problem in variational Hodge theory and partially answered by Bloch in [1]. We answer the question in terms of a Brill-Noether type locus associated to the invertible sheaf corresponding to the divisor.

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